Question

. In the following figure, the side BC of ∆ ABC is extended up to the point D. If ∠ A = 55° and ∠ B = 60°, then the measure of ∠ACD is
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Answer 1

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Answer 2

Given :   side BC of ∆ ABC is extended up to the point D

∠ A = 55° and ∠ B = 60°

To Find :  the measure of ∠ACD is

Solution:

Sum of angles of a triangle is 180°

=> ∠ A  + ∠ B   + ∠ C  = 180°

Substitute ∠ A = 55° and ∠ B = 60°

=> 55° + 60° + ∠ C  = 180°

=> ∠ C + 115°  = 180°

∠ C  is ∠ACB

=>   ∠ACB  + 115°  = 180°

Now ∠ACB  and ∠ACD form a linear pair as BC is extended to D

=> ∠ACB + ∠ACD = 180°

Equate both Equations:

∠ACB + ∠ACD =  ∠ACB  + 115°

=> ∠ACD =   115°

Hence  the measure of ∠ACD is 115°

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